Mood music: The xx are looking on the glossier side of life as they begin a tour

With a number-one album and fans including Rhianna and Samantha Cameron, it's been a stellar year for The xx. Craig McLean catches up with the enigmatic Londoners who helped provide the soundtrack to 2012.

Three hours before showtime in Utrecht, and the British band of the year are perched, like the crows on the telephone wire in Dumbo, along their dressing-room sofa. Here's Romy Madley Croft, 23, one of The xx's two singers, and the south-London trio's guitarist. Like her bandmates, she's friendly, thoughtful and quiet. She's talking about last night's show in Antwerp, when The xx played to a whopping, whooping 7,500 people, their first arena crowd.

"Yesterday definitely took our breath away," she says softly. "We've played some big festivals, on some pretty big stages, and played to – how many people in Belgium? 40,000? Which made me feel insane. But to come back and play our own arena show – last night was the biggest [headline] show we've ever played – that made me feel a bit crazy. It looked like [London's] O2, but scaled in a bit."

Next to her, in the middle, is Oliver Sim, 23, bass player and the other frontperson. His speaking voice, like his singing one, is low – so low that it often rumbles below hearing level. He's talking about the strength and succour this band of black-clad equals draw from their long friendships. In the case of he and Croft, they've known each other, via their mothers, since they were toddlers. They began playing music together at Putney's Elliott School (other musical alumni include: Hot Chip, Burial, Four Tet).

"I appreciate that more than ever. The idea of being in a band with people you don't even know…" he says with a small shudder. "Like some people just reply to an advert in NME – 'Drummer Wanted' – that just seems pretty alien to us. So, yeah, I definitely appreciate it a lot. I can't even imagine how it must be to be a solo artist playing with session musicians. I remember hearing an interview with [XL Recordings label mate] Adele saying that she finds touring the most lonely place in the world, and I felt so sorry for her."

And next to him, furthest away from me, is Jamie Smith, 23, aka Jamie xx, the band's drummer, multi-instrumentalist and sonic architect, and an in-demand DJ, producer and remixer (Florence and the Machine, Radiohead, Gil Scott-Heron). His voice is as elusive as his eye-contact. He's talking, just, about his skills. "I never really learnt from anyone. I just spent a lot of time at home, knocking things out. It has been interesting going into proper studios, working with people who know everything. But I find it doesn't hinder me. I was in the studio with Alicia Keys [for a track on her new album], and we were just experimenting with things, and she was quite interested in the way that I worked, just a laptop and keyboard, rather than this whole massive studio that we had. So, yeah," he repeats, unshowily, "it can be interesting."

What does he think these big-league collaborators are looking to get from him? "Some of them have told me. They like a certain melancholy that comes with our sound, and they want to find something that moves away from that overproduced American pop stuff. But at the same time they want some of that in there as well."

The xx have been touring since May, since finishing their second album, Coexist. It was released, to rave reviews (and going straight to number one in five countries), in September and is sure to figure near – or at – the top of many of the Best Albums of 2012 polls. Throwing more uptempo beats and fresh colours (steel drums!) into their artfully spartan sound, Coexist came out almost exactly three years since their debut – an equally lauded album that, a year later, won the 2010 Mercury Music Prize.

That night in London, they appeared on stage, blinking. Proper rabbits in the headlights. They had already had to deal with some difficulty – a fourth member, Baria Qureshi, had been asked to leave, for reasons the band still diplomatically decline to detail. But that night, and the concomitant avalanche of publicity, put them at a crossroads. "We felt genuinely as we looked," recalls Croft. "It was a shock, and it was amazing. It was our first awards thing. I was just thinking about going through the whole red-carpet thing, getting our pictures taken…"

That week, 12 months after its release, The xx album reached its highest point in the charts. "That was really nice," she continues. "The album had grown naturally; it wasn't like it came out and was a hit. And I guess we could have just gone back and done a big tour." But rather than cashing in on their success, The xx did one US tour and then "just went into hiding. We were pretty knackered by that point and felt like we were ready to start making new music."

Sim nods. "A big part of the excitement about the Mercurys was that we were home for a week. That was the longest we'd been home for a while."

That self-titled debut was a wonder: an album of space and beauty and atmosphere, of spidery guitar lines and echoey electronics and simple soul, but also of indelible pop hooks. Its openness and its simplicity lent itself to all manner of "syncs". The xx became the sound of the BBC's coverage of the 2010 General Election, were featured in Gossip Girl, sampled by Rihanna (their track "Intro" opened her 2011 song "Drunk on Love"), and were used by advertisers and broadcasters and opportunists left, right and far right.

For these self-effacing, unassuming musicians who are precious (in the right ways) about their songs, does all that exposure taint their creations? A little, agrees Sim. "The ones you have control over [are OK] – the Rihanna one, that was something we approved and we liked. And some… I've turned on Channel 4 and heard us on shows like Embarrassing Bodies and not really understood what was going on."

"It's that thing where you don't have control over it any more," frowns Croft. When the band were first exposed to the music industry and how it worked, they were not long out of school. "It's what you learn through just doing it. When you sign over your music to the BBC or Channel 4, you are signing it over, and they either use it or they don't. And with our music, I kept getting texts from friends – 'Oh, you're on this, you're on this, you're on this…' – those weird programmes that it doesn't make any sense for you to be on."

To their discomfort, the Conservative Party Conference used "Intro", and the PM supposedly said that he and Sam Cam like to cuddle to The xx. Did the band believe that? Croft titters, while Sim grimaces.

"We try not to think about that," he eventually smiles. "The big thing that we're scared of is the idea of just being shoved in people's faces. It was like when Gotan Project became the sound of Boots. But when it comes to ones we have control over, our publishers have got it now – we're like the 'no' people." So The xx have declined "quite a lot" of advert offers. They think k they've said yes twice. One, early one, was for an AT&T Olympics advert.

"Which in retrospect we probably would have said no to now," shrugs Croft. "Then we went to America and did an interview, which was filmed, and I didn't know what AT&T was. I was really embarrassed. It's like BT or Vodafone in the US. So I feel like we've learnt a lot. When we started out we were young and were testing the water. Then," she remembers, "there was a fake version of [first album song] 'VCR'…"

"In Slovenia?" asks Sim.

"No, it was in a phone advert somewhere in Asia. It was a remade version."

"And there was an unapproved one for guns. It was American. The xx," he clarifies with a grin, "do not condone guns!"

After three heavy years of touring The xx have settled into an easy, functional, on-the-road routine. Tall, handsome, fit, fashion-forward Sim has given up beer, now favouring gin and tonic and regular physical work-outs. "Now we've got the luxury of being able to bring friends from home out with us – that makes it a lot more exciting."

His Rowenta portable valet idles on the dressing-room floor, near his open mobile closet of entirely tenebrous clothing, ready for another pre-show steaming. But while his wardrobe may have something of the night about it, the relaxed guitarist is affable, relaxed and engaged. When my Dictaphone threatens to play up, he records the interview on his iPhone, then emails it to me afterwards, along with a clip from the Katy Perry tour documentary (Part of Me) that we'd discussed at one point. "That bit made me feel so sorry for her," he said.

Small, smiley, striking, elegant Croft finds comfort in writing song whenever possible. "You can't really sit and start singing into a laptop at an airport. Well," she thinks, "you could, but you'd have a lot of sound in the background. I'm always trying to write stuff. Oliver and I both like writing at night, that time when you're half-awake, half-asleep. But we're travelling on a tour bus with bunkbeds right next to each other, so I can't sing into my laptop like I would in my bedroom and test out ideas. But it's just about adapting."

"I'm pretty envious of Jamie," adds Sim of Smith's music-making methods. "He can just put his headphones on and completely escape. It's a bit harder for me and Romy. We need the option to be alone and be quiet and still. And that doesn't come about very often on tour. Whereas he can be at an airport and just be lost in it."

Medium-height, dark-eyed, shy, undemonstrative, red-wine-drinking Smith, meanwhile, embraces all the opportunities touring throws his way. Tonight, after the show, he's DJing from midnight until 2am in a local club. Plus, his girlfriend is on the road. "We have a rule that we don't go more than a week apart," the friendly and fragrant Italian says when we bump into her in a backstage corridor. "We had to go three weeks in the summer and we nearly went mental."

He goes under the name Jamie xx because, when he plays clubs or works with other artists, he's carrying the whole band with him. "And we all have the same musical values. But also," he says with a hint of a smile, "the name came about cos I couldn't think of a better one."

Enigmatic. Melancholy. Sad. Minimal. These are the adjectives you're meant to use when talking about The xx. They are these things, sometimes, for sure. But there is real, pure, palpable joy about them. For all the heartache – real, experienced and/or imagined – in Croft and Sim's lyrics, there's a euphoria too. The xx are resolutely not post-millennial Joy Division, pretentious emos, woe-is-me goths or dour indie refuseniks. They're pop fans and club-goers who just happen to view quieter music as the perfect prism through which they can talk about the delicate, shifting, sometimes abstract matters of the heart.

But give them half a chance and they'll shake a tail-feather. After all, this is a band who, to a (wo)man, worship at the feet of Beyoncé. They love Sugababes and Drake, and Rihanna and Lady Gaga. But Beyoncé is the one, and they are thrilled at having met her a couple of times (once in London after the Radio 1 Hackney Weekend in the summer). They've even, Sim has said, written with the Queen B in mind. "Did I say that?" he gulps, slightly startled, looking at Croft. "Um… we've written a song, yeah, together, the three of us, in the past three months. It's good. To be honest, I'm just excited that we're able to work on tour," he deflects.

"It's just writing," chips in Croft, riding to the rescue of her closest friend. "And we've written some stuff that we've thought, 'Oh, that would be amazing if that could be sung by this person…' Just pushing ourselves in different directions. Trying to write with the intention of it not being sung by ourselves. That's something that is quite fun.

"But, just, kind of, yeah…" she falters. "I wouldn't say anything like, 'Yes, message to Beyoncé, we have a song for you…' But if it happens that would be incredible."

So just to be clear: did you write with her in mind? "We definitely weren't trying to put ourselves in Beyoncé's shoes and write a song!" Sim declares. "It was just that we wrote something, and liked it, and felt like we could… give it up, I suppose."

Can they tell us the title? Croft and Sim look at each other. As happens on stage, when they face each other with their instruments and stalk the stage together, something almost telepathic seems to pass between them.

Croft [quickly]: "No."

Sim [catching up]: "No."

"You were about to say it!" she laughs to him. Sim just looks at her, his eyes boggling a little.

On stage a couple of hours later, The xx bedazzle, bewitch and, you might say, Beyoncé, 2,500 Dutch fans. Courtesy of the sexed-up R&B beats with which Smith has retooled some of their songs, there is more booty-shaking than head-nodding. And even some hands in the air. The lights wink and glimmer, in perfect sync with the music. Images based on their xx logo – designed by one-time art student Croft – beam down from screens.

The voices of childhood friends Croft and Sim weave around each other in lifelong empathy. It's a total, immersive concert experience, magical and transporting. It's no wonder that their most recent album is called Coexist. They are all, band and fans, in this together.

Earlier, asked for their individual highlights of their stellar year, The xx had each thought hard.

Jamie Smith said it was the morning in May when he finally handed in the finished album, after two or three sleepless nights, at 6am, had a big fry-up, then promptly went on holiday to Majorca. "That was the first time I finished the album," he clarified, lips twitching. "There was another month or so after that."

Oliver Sim said it was walking down London's Oxford Street with Romy Madley Croft, going into HMV, and seeing a giant poster advertising their imminent album. "There was no backing away from it then – we couldn't finish it again."

For Croft, it was playing in Australia and hearing people singing new song "Angels" back at them. "It was so loud!" she gasped, still shocked. "They were shouting – I guess that chorus is pretty… shoutable. That moment it felt like, 'OK, it's changing.' I was so excited."

And their hopes for 2013?

More writing on tour, "to definitely up the creativity level compared to last time", said Croft. "I'd like to play in South America," says Sim. "Same as Romy, really," says Smith.

The UK tour starts on Thursday at the Dome in Brighton. The album 'Coexist' and the single 'Chained' are both out now on XL Recordings